Simple Pendulum and SHM

Galileo's Lamp
Galileo’s Lamp (Pisa Cathedral)

Galileo showed that the motion of a swinging pendulum is ISOCHRONOUS – amplitude is independent of time period T.

Without derivation, it can be shown that

Screen Shot 1.png

for a simple pendulum

The rules for measuring oscillations are as follows:

  • rigid support
  • heavy bob
  • massless string
  • measure l to the centre of the weight
  • small oscillations (less than 5 degrees either side – or amplitude less than l/6)
  • count 10 or more oscillations from the CENTRE or 0 of displacement, seen against a vertical fiducial mark, 0,1,2,3….and so on, divide by 10 to get T.
  • repeat as time permits.

You are penalised for not drawing a labelled table of results including headers, units, repeats and treatment of errors if appropriate.

In the absence of damping forces tending to decrease amplitude and increase time period, for small oscillations (angle of swing less than 5 degrees) the oscillation is simple harmonic.

You will do an experiment in the lab to show that T2  and l are directly proportional. Here are some specimen results.

Calculate the slope of the graph. Use it to work out a value for g since gradient =  4 π2/g

This applet contains  more than we need, but it’s worth a  look. You can change l, m and g.

Knowing that SHM is executed and by definition:

Screen Shot 4.png

at the extremities of the oscillation, the force toward the centre is maximum, hence a is maximum and proportional to x.

knowing that

Screen Shot 7.pngScreen Shot 5.png

Screen Shot 6

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s